Cosmological sheets, or pancakes, form as overdense regions
collapse preferentially along one axis. Originally studied by
Zel'dovich [59] in the context of neutrino-dominated cosmologies, sheets are
ubiquitous features in nonlinear structure formation simulations
of CDM-like models with baryonic fluid, and manifest on a
spectrum of length scales and formation epochs. Gas collapses
gravitationally into flattened sheet structures, forming two
plane parallel shock fronts that propagate in opposite
directions, heating the infalling gas. The heated gas between the
shocks then cools radiatively and condenses into galactic
structures. Sheets are characterized by essentially five distinct
components: the preshock inflow, the postshock heated gas, the
strongly cooling/recombination front separating the hot gas from
the cold, the cooled postshocked gas, and the unshocked
adiabatically compressed gas at the center. Several numerical
calculations [15,
52,
8] have been performed of these systems which include the baryonic
fluid with hydrodynamical shock heating, ionization,
recombination, dark matter, thermal conductivity, and radiative
cooling (Compton, bremstrahlung, and atomic line cooling), in
both one and two spatial dimensions to ascert the significance of
each physical process and to compute the fragmentation scale.

In addition, it is well known that gas which cools to
through hydrogen line cooling will likely cool faster than it
can recombine. This nonequilibrium cooling increases the number
of electrons and ions (compared to the equilibrium case) which,
in turn, increases the concentrations of
and
, the intermediaries that produce hydrogen molecules
. If large concentrations of molecules form, excitations of the
vibrational/rotational modes of the molecules can efficiently
cool the gas to well below
, the minimum temperature expected from atomic hydrogen line
cooling. Because the gas cools isobarically, the reduction in
temperature results in an even greater reduction in the Jeans
mass, and the bound objects which form from the fragmentation of
cooled cosmological sheets may be associated with massive stars
or star clusters. Anninos and Norman [7] have carried out 1D and 2D high resolution numerical
calculations to investigate the role of hydrogen molecules in the
cooling instability and fragmentation of cosmological sheets,
considering the collapse of perturbation wavelengths from 1 Mpc
to 10 Mpc. They find that for the more energetic (long
wavelength) cases, the mass fraction of hydrogen molecules
reaches
, which cools the gas to
eV and results in a fragmentation scale of
. This represents reductions of 50 and
in temperature and Jeans mass respectively when compared, as in
Figure
6, to the equivalent case in which hydrogen molecules were
neglected.

Figure 6:
Two different model simulations of cosmological sheets are
presented: (a) a six species model including only atomic line
cooling, and (b) a nine species model including also hydrogen
molecules. The evolution sequences in the images show the
baryonic overdensity and gas temperature at three redshifts
following the initial collapse at
z
=5. In each figure, the vertical axis is 32 kpc long (parallel to
the plane of collapse) and the horizontal axis extends to 4 Mpc
on a logarithmic scale to emphasize the central structures.
Differences in the two cases are observed in the cold pancake
layer and the cooling flows between the shock front and the cold
central layer. When the central layer fragments, the thickness of
the cold gas layer in the six (nine) species case grows to 3
(0.3) kpc and the surface density evolves with a dominant
transverse mode corresponding to a scale of approximately 8 (1)
kpc. Assuming a symmetric distribution of matter along the second
transverse direction, the fragment masses are approximately
() solar masses.